Satellite-airborne-terrestrial edge computing networks (SATECNs) emerge as a global solution for Internet of Things (IoT) applications in 6G which require massive use of artificial intelligence such as autonomous driving, industrial Internet of Things (IIoT), and telemedicine. Moreover, they can provide global coverage even in remote areas and under natural disasters through emergency communications. However, satellite networks are highly dynamic and their varying topology and network traffic make their management and control challenging. In this thesis, we investigate dynamic computing resource allocation, task offloading, and power allocation for IoT devices, UAVs, and satellites equipped with edge computing capabilities to minimize the Age of Information (AoI) and energy consumption. Since the data freshness optimization requires timely decisions, we present a new lifelong learning algorithm (LL-SATEC) that adapts to the environment by exploiting knowledge transfer between devices in different layers in SATECNs. Lifelong learning is a promising machine learning algorithm that learns continuously without requiring a new training phase every time the network condition changes. In addition, we exploit the heterogeneity of devices and network layers in SATECNs to define different learning domains and perform cross-domain lifelong learning (CDLL-SATECNs). As a result, we obtain resource allocation policies online for IoT devices, UAVs, and satellites that optimize the AoI and energy. Numerical results indicate that our approach significantly accelerates learning compared to traditional reinforcement learning algorithms. Specifically, it reduces the average AoI by 65% and the average energy consumption by 50%, achieving these improvements within just a few iterations and without suffering from catastrophic forgetting.